Suppose I have the following function

`G[n_, k_] := Product[g[n + i]/g[i], {i, 0, k}] `

where $ n,k$ are assumed to be natural numbers and $ g$ is a nonzero symbolic function. I want to simplify the expression `G[n,k+1]/G[n,k]`

and cancel all common terms to get `g[n+k+1]/g[k+1]`

. However, `Simplify`

, `FullSimplify`

, `Expand`

and `Cancel`

all yield the symbolic (not cancelled) product.